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http://dx.doi.org/10.11568/kjm.2016.24.4.723

BOUNDEDNESS IN NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY  

Im, Dong Man (Department of Mathematics Education Cheongju University)
Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Korean Journal of Mathematics / v.24, no.4, 2016 , pp. 723-736 More about this Journal
Abstract
This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.
Keywords
h-stability; $t_{\infty}$-similarity; bounded; nonlinear nonautonomous system;
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Times Cited By KSCI : 3  (Citation Analysis)
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